Determination of |V<em>_cb</em>| and form factors of <em>B̄⁰ → D*⁺ℓ⁻</span>ν̄_ℓ</em> decays with Belle II data

Abstract

<p>This thesis presents a determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element magnitude |<em>V_cb</em>| and form-factor parameters of <em>B̄⁰ → D^*+ℓ⁻ν̄</em>_ℓ decays, where ℓ = <em>e</em>, <em>μ</em>. We conduct our analysis using Belle II data collected from 2019 to 2021, corresponding to an integrated luminosity of 189fb⁻¹. In the Belle II experiment, electrons and positrons collide with a center of mass energy 10.58 GeV, which corresponds to the <em>Υ</em>(4<em>S</em>) mass. Subsequently, more than 96% of <em>Υ</em>(4<em>S</em>) mesons decay to <em>BB̄</em>. We reconstruct signal <em>B̄</em>⁰ → <em>D</em>^*+ℓ⁻<em>ν̄</em>_ℓ decays, followed by <em>D</em>^*+ → <em>D</em>⁰<em>π</em>⁺ and <em>D</em>⁰ → <em>K</em>⁻<em>π</em>⁺ decays, without explicitly reconstructing the accompanying <em>B</em> meson produced in the <em>Υ</em>(4<em>S</em>) decay. <br /> The theoretical description of the differential decay rate of the <em>B̄</em>⁰ → <em>D</em>^*+ℓ⁻<em>ν̄</em>_ℓ channel relies on kinematic variables that are intimately related to the momentum of the <em>B</em> meson. However, due to the escape of final-state neutrinos from the Belle II detectors, it is challenging to precisely measure the momentum of the <em>B</em> meson. To address this problem, we have developed a novel approach for inferring the kinematic variables. This approach leverages the angular distribution of the signal <em>B</em> meson as well as particles produced by the accompanying <em>B</em> meson. Compared to previous methods, our novel approach improves the resolution of the reconstruction by 7% to 12%.<br /> The determination of the signal yield in each bin of the kinematic variables includes a two-dimensional binned fit to the distributions of cos <em>θ_BY</em> and <em>ΔM</em>. Here, <em>θ_BY</em> represents the angle between the <em>B</em> candidate and the <em>D</em>^*ℓ</span> system (denoted as <em>Y</em>), while <em>ΔM</em> is the mass difference between the <em>D</em>^*+ and <em>D</em>⁰ candidates. Because of the detector resolution, the observed signal yields may deviate from the underlying true yields. To correct for this distortion, we employ the singular-value-decomposition unfolding method. Subsequently, partial decay rates in bins of kinematic variables are derived from the unfolded yields and reconstruction efficiencies, which are estimated using simulated samples.<br /> By summing the partial decay rates over kinematic bins we obtain the total rate. The average of the total rates over two decay channels is converted to branching fractions using the <em>B</em>⁰ lifetime. We find <em>BR</em> = (4.922±0.023±0.220)%, which is compatible with the world average. We fit to the partial decay rates on four projections simultaneously to determine the values of |<em>V_cb</em>| and form factor parameters in the Boyd-Grinstein-Lebed and Caprini-Lellouch-Neubert parameterizations, respectively, and find |<em>V_cb</em>|_BGL = (40.57±0.31±0.95±0.58) × 10⁻³ and |<em>V_cb</em>|_CLN = (40.13±0.27±0.93±0.58) × 10⁻³, where the uncertainties are statistical, systematic, and the component due to lattice QCD inputs, respectively. The leading and subleading systematic uncertainties arise from the slow pion tracking efficiency and the ratio of <em>B</em>⁺<em>B</em>⁻ pairs and <em>B</em>⁰<em>B̄</em>⁰ pairs in the <em>Υ</em>(4<em>S</em>) decay, respectively.<br /> In addition, we assess lepton flavor universality by examining three important variables, including the ratio of branching fractions and differences in lepton angular asymmetry <em>A_FB</em> as well as the longitudinal <em>D</em>^* polarization fraction <em>F_L</em> between <em>B̄</em>⁰ → <em>D</em>^*+<em>e</em>⁻<em>ν̄</em>_<em>e</em> and <em>B̄</em>⁰ → <em>D</em>^*+<em>μ</em>⁻<em>ν̄</em>_<em>μ</em> decays. We find the ratio <em>R_e/μ</em> = 0.998 ± 0.009 ± 0.020 and differences <em>ΔA</em>_FB = (−17±16±16) × 10⁻³ and <em>ΔF_L</em> = 0.006 ± 0.007 ± 0.005, where the first and second uncertainties are statistical and systematic, respectively. All results align with the expectations of lepton flavor universality within the Standard Model.